Norvbin 



propeller; again, that drag may well be increased by a factor of 3 

 if the propeller is locked. 



The characteristics of a propeller in axial open-water flow 

 are usually given by tables or curves of well-known Ky and Kq 

 coefficients versus advance ratio J. In yawed flow the propeller 

 also experiences a lateral force and a (small) pitching moment, [ 58] . 



In behind conditions the effective angle of drift at the pro- 

 peller still is roughly 2/3 of the nominal local angle, high enough to 

 let the propeller contribute the fin effect already mentioned. (The 

 sidewash behind the propeller then has a further straightening effect 

 on the flow to the rudder.) The effective advance ratio is modified 

 by the effective wake in the factor 1 - w; here w will be chosen as 

 for thrust identity. The effective wake, again, is modified by the 

 drift of the ship, being higher for a starboard drift angle than for a 

 port one and a right-handed propeller [ 59] ; here that effect will be 

 taken as of second order. 



Finally, the vertical asymmetry of the flow field is responsible 

 for the appearance of a lateral force on the propeller of a ship even 

 if drift or yaw are zero. In case of a single screw ship this latter 

 force may be put equal to 3 to 5 per cent of the thrust, [ 60] . A 

 right-handed screw tends to throw the stern of a loaded ship towards 

 starboard, thus requiring a small starboard helm to be carried on 

 straight course. Other free-running model tests prove that draught 

 conditions may change this picture, and that the ship on light draught 

 may have a tendency to turn to starboard, [ 6i] , 



The hydrodynamic thrust T (Tg, Tg, Tp) and torque Q 

 (Qc Qg, Qp) — which is negative in case of a right-handed screw on 

 a driving shaft — will be given as quasi- stationary functions of 

 instantaneous values of forward ship speed, u, and screw r.p.s. , 

 n (ng, n^ , np) . The thrust is a major factor governing the flow 

 velocity past the rudder, and this velocity likewise will be given in 

 terms of u and n. Rudder control derivatives usually are deter- 

 mined from model tests in one or two conditions of screw loading 

 only. In order to find an adequate prediction of full scale control 

 derivatives for the more general propulsion case it is necessary to 

 combine model results with a simple procedure for calculating the 

 total control force due to rudder deflection. 



From the hydro dynamical point of view the typical all- 

 movable rudder in behind condition is equivalent to a twisted wing 

 on a pointed afterbody. There are a number of additional complica- 

 tions , however: The spanwise velocity distribution is highly non- 

 uniform, the flow along the chord is accelerating or decelerating, 

 the gap between wing and body is within a retarded boundary layer 

 flow and it also varies with the angle of deflection, the boundary 

 conditions at the free surface violate the vertical symmetry aspect 

 even if there is no suction-down of air, the shape of the body stern 



856 



